We rise the framework of recently formulated kinetic model of temperature-dependent processes accompanying the recording and erasure of diffraction gratings in a polymer matrix doped with azobenzene chrompohores under the illumination with spatially modulated and linearly polarized light to study general features of temperature dependence of tinge evolution of diffraction efficiency close to the glass transition. temperature T-g of the polymer matrix. Bond fluctuation Monte Carlo simulations are used. Basic kinetic results found in simulations are in agreement with preliminary experimental results obtained in degenerate two-wave mixing (DTWM) experiment. We discuss, using Monte Carlo results, the concept of temperature controlled writing of diffraction gratings in a temperature interval close to T-g.